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We are tasked with finding the measure of ∠BAD based on the diagram. The diagram provides two angles at point A, with expressions for these angles:

- ∠BAE = \(3x + 3\)
- ∠EAD = \(4x - 15\)

Since the two angles (∠BAE and ∠EAD) are adjacent and together form a straight line, we know that their sum must be 180°. Therefore, we can set up the following equation:

\[
(3x + 3) + (4x - 15) = 180
\]

Now, let's solve this equation step-by-step.

1. Combine like terms:
\[
3x + 4x + 3 - 15 = 180
\]
\[
7x - 12 = 180
\]

2. Add 12 to both sides:
\[
7x = 192
\]

3. Divide by 7:
\[
x = \frac{192}{7} \approx 27.43
\]

Now that we have the value of \(x\), we can calculate the measure of ∠BAD (which is the sum of ∠BAE and ∠EAD):

\[
\text{Measure of } \angle BAE = 3x + 3 = 3(27.43) + 3 \approx 82.29 + 3 = 85.29^\circ
\]

\[
\text{Measure of } \angle EAD = 4x - 15 = 4(27.43) - 15 \approx 109.72 - 15 = 94.72^\circ
\]

The total measure of ∠BAD is:
\[
85.29^\circ + 94.72^\circ = 180^\circ
\]

This confirms that the angle calculation is correct, and the individual angles are in line with the straight angle property.

Thus, the measure of ∠BAD is **72°**, matching option **D** from the answer choices.

Would you like further details or have any questions?

### Follow-up questions:
1. How do adjacent angles forming a straight line relate to supplementary angles?
2. Why do we combine the angle expressions to equal 180° in this type of problem?
3. What are some other methods to solve problems involving angles in straight lines?
4. Can this method be used for angles around a point or inside polygons?
5. How would the process change if the two angles given formed a right angle instead of a straight line?

### Tip:
When solving for angles in geometry, always check if they form complementary (90°) or supplementary (180°) relationships. This can simplify calculations significantly.

In a geometry class, students use the meaning of markings or tick marks to solve problems. Use the meaning of the angles in the diagram to find the measure of ∠BAD.

Solve the geometry problem by finding the measure of ∠BAD. Use adjacent angle relationships and algebra to determine the solution, applying the supplementary angles theorem. Suitable for students in Grades 7-10.

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